Jack Halpern University of Chicago
Chicago, Illinois 60637
I I
Some Aspects of Chemical Dynamics in Solution
M a n y of the concepts pertaining to the dynamics of reactions in the gas phase are applicable also to reactions in liquids. The rates of reactions are expressed by rate laws, similar to those for gas phase reactions, reflecting the facts that the rates in both cases are related to the rates of encounters between reactants and are governed by similar energetic and configurational constraints. Indeed, for certain simple reactions, notably those involving relatively nonpolar reactants, such as the decomposition of nitrogen pentoxide or of di-t-butyl peroxide and the dimerisation of cyclopentadiene, the values of the rate constants and of the activation parameters in various solvents are strikingly close to those in the gas phase (1). Notwithstanding these parallels, there are also many important differences between the dynamic behavior of reactions in the gas and liquid phases. The solvent may influence the course of a reaction in solution in a variety of ways, among them the following. (1) Solvation of the Reactants and/or Intermediate Species Including the Activated Complex. Such effects are particularly important in reactions involving ions and/or polar molecules for which solvation energies can be quite large. Indeed, the occurrence of separated chemically stable ionic species under ordinary conditions is essentially confined to solvents of high dielectric constant and i t is only in such media that similarly charged ions can approach each other to within normal reacting distances with reasonably low activation energies. This is illustrated by the simple electron transfer reaction between Fez+ and (isotopicallylabeled) Fea+ions,
which occurs in aqueous solution with an activation enthalpy of only 9.3 lccal/mole and an activation freeenergy of 16.3 kcal/mole a t O°C (@. These values are compatible with the mutual approach of the reactant ions to within an internuclear separation of about 7A (corresponding to the estimated point of contact of the first coordination shells) for which the Coulomb repulsion free energy is estimated (using the bulk dielectric constant of water, i.e., 80) to be only 4 kcal/mole. I n the gas phase (or in a liquid medium of very low dielectric constant) the corresponding Coulomb repulsion free energy for comparable approach would amount to several hundred kcal/mole. (2) Participation in the Reaction; e.g., as a Nucleophile. Numerous examples of such participation are known, one being the substitution reaction (dien = diethylenetriamine), 372 / Journal of Chemical Education
This reaction (5) proceeds in aqueous solution according to the rate law (which is characteristic also of the substitution reactions of other square-planar complexes), Rate
kr[Pt(dien)C1+]+ kl[Pt(dien)Cl+][Br-]
=
(3)
The second (i.e., k!) term in the rate law is attributed to the direct replacement of C1- by Br-, whereas the first term is believed to arise from the indirect replacement path,
+ H1O
Pt(dien)CIC Pt(dien)OH?+
+ Br-
-
Pt(dien)OH?+
+ Pt(dien)Bri
+
C1(rate determining) (4)
+ HzO
(5)
(3) Participation of the Solvent as a Proton Acceptor and/or Donor. Examples of such participation are provided by certain proton transfer reactions in aqueous solution, e.g.
for which proton-transfer through one or more intervening water molecules by a Grotthuss-type mechanism, i.e.,
has been shown to be an important path (4). Closely related to this theme are the mechanisms of proton conduction in water and other protolytic solvents, as well as certain aspects of acid-base catalysis (6). Finally, another important difference between the dynamics of reactions in gases and liquids relates to differences between the duration of encounters in the two phases. Some of the consequences of this are considered in the following sections. Encounters and Collisions in Liquids: Diffusion-Controlled Reactions
The duration of an encounter between two noninteracting molecules in the gas phase is very short. Thus, following a collision between them, two molecules are likely to separate and the probability of two or more successive collisions between the same pair of molecules is small. In the liquid phase, on the other hand, a pair of molecules or ions which diffusetogether are constrained from separating by the "cage-effect" exerted by the surrounding molecules and they generally stay together as nearest neighbors for a relatively long time. I n a solvent such as water the duration of this cage-lifetime for a pair of noninteracting species is of the order of lo-" sec, during which they may undergo between ten and several hundred collisions with each other ( 6 , 7 ) .
The consequences of this are obviously important, particularly for reactions which tend to occur a t nearly every collision between reactants. The rate constants for such reactions will approach the upper limit determined by the rate constant k ~ for , diffusional encounters between reactants. The latter can be computed from the Smoluchowski-Debye equation (8)which can be approximated as,
where
is the separation of closest approach of the reactants A and B DABis the mean diffusion coefficient of the reactants N is Avogadro's number Z Aand ~ Zse are the reactant charges k is the Boltzmann constant T is the absolute temperature r is the dielectric constant CAB
The value of kD in aqueous solution is of the order of lo9-10IOM-' sec-' for neutral molecules and somewhat lower or higher for two ions depending on whether their charges are similar or opposite. kDrepresents an upper limit for the rate constants of bimolecular reactions in solution which is approached by reactions occurring a t nearly every encounter. Such reactions are said to be diffusion- or encounter-controlled and their activation energies are characteristically in the range 3-5 kcal/ mole corresponding to the activation energy for diffusion in liquids. Some examples of diffusion-controlled reactions are listed in the table. Many protontransfer reactions belong in this class. Some Diffusion-Controlled Reactions
--
Second order rate constant Refer(M-'seo-') ence
Reaction
+ ++ +
H,O+ OH2HIO H,O+ + CH,COO-- CHICOOH H.O+ NIT8 NH4+ HIO NH,+ 011NHI H1O Cu2+ e,,- + Cuf 0 s e,,0%F e ( C N ) P e.,Fe(CN)s4OH+I--OH-+I 21 19
+
-
+
-
++
+ HzO
a This rate constant, the highest known for any bimolecular reaction in solution, is rappreciably greater than that calculated far diffusional encounters between HaO+ and OH- ions. The explanation for this, as well as for the high rate constants found for certain other proton transfer reactions, is probably that proton transfer between H,O+ and OH- occurs when the ions are still separated by two water molecules or, effectively, between HQO,+ and H704- ions (6). e.,- represents the hydrated electrons. Rate constants taken from a compilation in ref. (33). In CC14;other reactions are in water.
Elementary Reactions
Consider an elementary bimolecular reaction in solution represented by,
the forward and reverse rate constants being related by, kdk. = K-, (11) Taking account of the diffusional encounter processes referred to above, the simplest detailed mechanism that can be written for the reaction must include a t least three steps,' i.e.
(A---B) and (G--D) denote the reactant and product collision complexes whose life-times, because of the cage effects, will generally be sufficiently long to justify considering them as intermediates. Provided that the concentrations of these collision complexes are low, the usual steady-state approximation can be applied, and yields the result,
Several limiting cases of this kinetic pattern may be realized, corresponding to each of the three terms in the denominator becoming much larger than the other terms which can, accordingly, be neglected. These limiting cases correspond to: [(kdk,)
(i)
+ (k-~k-~/k~k.)l
